The Phial of Galadriel, also known as Galadriel's jewel, also known as the star-glass, is a gift that Galadriel gives to Frodo as he leaves Lothlórien in The Fellowship of the Ring. It is a crystal that glows with the light of the elves' favorite star, Eärendil (the Morning and Evening star).
Like the name of Elbereth (which Frodo uses as a weapon against the Ringwraiths in The Fellowship of the Ring), the light from this star-glass is harmful to all things evil. Remember how Gollum can't eat lembas bread because it's an elf product and he is an evil creature? The light of the star-glass is like that times a million. It actually burns evil things.
But Frodo avoids using it for much of his trip into Mordor because a bright elf-star is not exactly going to go unnoticed in a place like the Dead Marshes. A shining beacon of goodness would kind of stand out in the middle of the Enemy's territory, right?
Where the Phial of Galadriel really comes in handy is Shelob's lair. When all seems lost as Shelob scuttles ever closer, Sam suddenly feels as though an image of the star-glass is taking shape in his own mind. With this inspiration, he shouts:
"Master, master!" cried Sam, and life and urgency came back into his voice. "The lady's gift! The star-glass! A light to you in dark places, she said it was to be. The star-glass!"
"The star-glass?" murmured Frodo, as one answering out of sleep, hardly comprehending. "Why yes! Why had I forgotten it? A light when all other lights go out! And now indeed light alone can help us." (4.9.27-8)
The star-glass hurts Shelob (though it isn't enough to kill her by itself). What's more, the star-glass seems to be Tolkien's way of representing some kind of holy spirit outside of any specific real-world religious framework. Sam is inspired to use the star-glass by a mysterious vision, rather than thinking of it in a practical way. And when he holds up the star-glass to fight Shelob, Sam feels someone speaking Elvish through him. It's as if the star-glass is some kind of direct access to divine powers. Now that's a handy present.